Algebra I Regents Practice Test

Questions and Answers

What is the correct formula to solve for the distance $r$ in the gravitational force equation $F = \frac{G M_1 M_2}{r^2}$?

$r = \frac{G M_1 M_2}{F}$

$r = \sqrt{\frac{G M_1 M_2}{F^2}}$

$r = \sqrt{\frac{G M_1 M_2}{F}}$ (correct)

$r = \frac{F}{G M_1 M_2}$

If the width of a rectangular flower bed is half of its length and the total area is 38 square feet, what is the equation that represents this relationship?

$L \cdot L = 38$

$L \cdot \frac{L}{4} = 38$

$L \cdot \frac{L}{2} = 38$ (correct)

$L^2 = 76$

Which cost equation represents Buffalo Party Rental for $x$ square feet of tent space?

$B = 6x + 25$

$B = 5x + 50$ (correct)

$B = 50 + 6x$

$B = \frac{5}{x} + 50$

What is the setup fee charged by Tent Genie?

$25$ Signup and view all the answers

For Buffalo Party Rental to be cheaper than Tent Genie, what inequality must be solved?

$5x + 50 < 6x + 25$ Signup and view all the answers

To the nearest tenth, what would the width of the flower bed be if the area is 38 square feet and the width is half of the length?

$5.0$ feet Signup and view all the answers

What variable represents the total cost for Tent Genie based on the tent space ordered?

$T$ Signup and view all the answers

If a couple orders 40 square feet of tent space from Buffalo Party Rental, what will their total cost be?

$250$ Signup and view all the answers

What is the solution set for the inequality $4x + 2 < 2(x + 5)$?

$x < -6$ Signup and view all the answers

Which equation correctly represents Arielle's situation of two numbers where the second number is seven less than twice the first?

$x + (2x - 7) = 45$ Signup and view all the answers

Which of the following statements about the enrollment function $E(x)$ is true?

$a = 3810$ and $b = 0.035$ Signup and view all the answers

What is the equivalent form of the trinomial $x^2 - 14x + 49$?

$(x - 7)^2$ Signup and view all the answers

Which of the following points does not lie on the graph of $f(x) = x^2 - 3x + 4$?

(-1, 6) Signup and view all the answers

Which of the following sequences are classified as arithmetic?

2, 4, 6, 8, 10... Signup and view all the answers

What is the form of the profit function from Carmelo's lemonade stand?

$L(c) = 0.82c$ Signup and view all the answers

Which expression is simplified correctly?

$5 imes √5$ Signup and view all the answers

Which function could represent a graph with roots at $x = -3$, $x = -1$, and $x = 1$?

$f(x) = (x + 3)(x + 1)(x - 1)$ Signup and view all the answers

What property justifies simplifying $12x^2 - 7x = 6 - 2(x^2 - 1)$ to $12x^2 - 7x = 6 - 2x^2 + 2$?

Distributive property of multiplication over subtraction Signup and view all the answers

Which inequality models the height, $h$, for the Little Tikes EasyScore Basketball Hoop?

$45 ewline ≤ h ≤ 60$ Signup and view all the answers

Which situation can be modeled by a linear function?

A concert venue allowing 20 people every 30 minutes Signup and view all the answers

What percentage of parents who preferred remote learning are middle school parents if the data shows

38.2 Signup and view all the answers

If a polynomial function has real roots, which of the following could NOT represent such a function?

$f(x) = (x + 1)(x^2 + 1)$ Signup and view all the answers

What is the solution to the inequality $x + 5 < 10$?

$x < 5$ Signup and view all the answers

What does the correlation coefficient suggest about the relationship between the number of hours studied and test scores?

More hours studied generally leads to higher test scores. Signup and view all the answers

Which of the following equations represents the total value of coins deposited by Mr. Rogers?

$0.10d + $0.25q = $17.55$ Signup and view all the answers

If Mr. Rogers deposited 90 coins in total, which system of equations would you use to find the number of dimes and quarters?

$d + q = 90$ and $0.10d + 0.25q = 17.55$ Signup and view all the answers

What is the consequence of replacing all dimes with quarters for Mr. Rogers?

He will not have enough money to buy the cardigan after tax. Signup and view all the answers

What does region A represent in the context of the inequalities graphed?

Combinations of dimes and quarters that meet a specific criterion. Signup and view all the answers

What is the main purpose of performing linear regression on the data set?

To draw a line that best fits the data to make predictions. Signup and view all the answers

What should Mr. Rogers include in his calculations when determining his total money for the cardigan?

The base price plus 8% sales tax. Signup and view all the answers

What does the gray region represent in the system of inequalities?

Values that satisfy both inequalities. Signup and view all the answers

Which expression is an equivalent form of $y^4 - 100$?

$(y^2 + 10)(y^2 - 10)$ Signup and view all the answers

What is the value of $f(16)$ for the function $f(x) = 2x^2 - 3 ext{√}x$?

307 Signup and view all the answers

Which of the following relations is not a function?

A set of points with two y-values for one x-value Signup and view all the answers

Given the function $g(x) = 2x^2 - 1$, what function $h(x)$ represents the result when $g(x)$ is translated 3 units to the right?

$2(x - 3)^2 - 1$ Signup and view all the answers

Which of the following expressions is equivalent to $6x^5 + 8x - 3x^3 + 7x^7$ when written in standard form?

$7x^7 + 6x^5 - 3x^3 + 8x$ Signup and view all the answers

Which equation and statement properly illustrate the approximate velocity of the motorcycle modeled by $V(x)$?

$V(x) = 4(1.35)!, and velocity is increasing$ Signup and view all the answers

Which of the following expressions results in a rational number?

$ ext{√}4 + 2$ Signup and view all the answers

Which statement about the function $h(x)$ obtained from $g(x)$ is true when translated to the right?

The x-values are shifted, affecting outputs. Signup and view all the answers

Study Notes